Quantum Backaction Evading Measurement of Collective Mechanical Modes

Ockeloen-Korppi, Caspar; Damskägg, Erno; Pirkkalainen, Juha-Matti; Clerk, Aashish A.; Woolley, Matthew J.; Sillanpää, Mika

doi:10.1103/physrevlett.117.140401

Cited by 107 publications

(76 citation statements)

References 44 publications

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“…The entangled photons at the heart of this phenomenon stem from the vacuum states of the constituent electromagnetic oscillators [8]. Indeed, entanglement from two-mode squeezing has also been extended to microwave photons in superconducting circuits [9], and even to hybrids composed of photons and phonons in optomechanical systems [10][11][12] where again the inputs comprise of vacuum states.…”

Section: Introductionmentioning

confidence: 99%

“…The demonstration of a correlation between two different mechanical resonators from parametric down-conversion, even in the classical limit, would indicate that extending this interaction to vacuum phonons should enable entanglements to be generated between two disparate solid state-state objects. Ultimately, access to such a state would be extremely desirable, as it would provide an invaluable platform in which to investigate the absence of quantum mechanical phenomena in our everyday classical world [12,[18][19][20]. Meanwhile, the ability to decipher classically correlated vibrations between spatially distinct mechanical resonators could be exploited to manipulate the vibrations of one of the resonators by measuring the vibrations of the other, thus further expanding the functionality portfolio of electromechanical resonators, as well as enabling systems with broken time-translation symmetry to be investigated [21].…”

Section: Introductionmentioning

confidence: 99%

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A correlated electromechanical system

et al. 2017

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A correlation with phonons sustained by a pair of electromechanical resonators that differ both in size and frequency is demonstrated. In spite of the electromechanical resonators being spatially distinct, they can still be strongly dynamically coupled via a classical analogue of the beam splitter interaction with a cooperativity exceeding five, and parametric down-conversion which results in both resonators self-oscillating. This latter regime yields a classical variant of a two-mode squeezed state which is identified as perfectly correlated phase-locked vibrations between the two resonators. The creation of a correlation between two separate mechanical resonators suggests that extending this interaction to vacuum phonon states could enable a macroscopic two-mode squeezed state to be generated. Conversely, the ability to resolve the correlated state via the self-oscillations could be harnessed to build a new class of detector where an external stimulus neutralises the phase-locked vibrations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A correlated electromechanical system

et al. 2017

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“…Nevertheless, there exist methods which can reduce the added arXiv:1902.05125v3 [quant-ph] 18 Jul 2019 noises of measurement below the SQL. For example, it has been recently shown [66] experimentally that in an optomechanical system with two mechanical modes one can achieve a measurement precision below the SQL based on a back-action evasion method.…”

Section: Introductionmentioning

confidence: 99%

Force sensing in hybrid Bose-Einstein-condensate optomechanics based on parametric amplification

et al. 2019

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In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the s-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). Furthermore, because of its large mechanical gain, such a modulated hybrid system is a much better amplifier in comparison to the (modulated) bare optomechanical system which can generate a stronger output signal while keeping the sensitivity nearly the same as that of the (modulated) bare one. The other advantages of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities are its controllability as well as the extension of amplification bandwidth.

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“…A crucial obstacle for a more widespread application of these techniques is the explicit time dependence of the driving electromagnetic fields. Dissipative preparation of mechanical states [4,[9][10][11][12][13][18][19][20][21][22][23][24][25] and tomographic backactionevading measurements of mechanical motion [26][27][28][29][30][31][32][33][34] rely on driving the system with multiple fields at different frequencies while parametric squeezing requires modulation of the optical spring [5,[35][36][37]; both of these approaches result in time-dependent optomechanical Hamiltonians. The steady-state Lyapunov equation can then only be applied under the rotating wave approximation (RWA) which neglects fast oscillating terms in the interaction and only keeps those that are resonant.…”

Section: Introductionmentioning

confidence: 99%

Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

2020

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Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators. In many applications, linearised form of the interaction is used, which allows for the system dynamics to be fully described using a Lyapunov equation for the covariance matrix of the Wigner function. This approach, however, is problematic in situations where the Hamiltonian becomes time dependent as is the case for systems driven at multiple frequencies simultaneously. This scenario is highly relevant as it leads to dissipative preparation of mechanical states or backaction-evading measurements of mechanical motion. The time-dependent dynamics can be solved with Floquet techniques whose application is, nevertheless, not straightforward. Here, we describe a general method for combining the Lyapunov approach with Floquet techniques that enables us to transform the initial timedependent problem into a time-independent one, albeit in a larger Hilbert space. We show how the lengthy process of applying the Floquet formalism to the original equations of motion and deriving a Lyapunov equation from their time-independent form can be simplified with the use of properly defined Fourier components of the drift matrix of the original time-dependent system. We then use our formalism to comprehensively analyse dissipative generation of mechanical squeezing beyond the rotating wave approximation. Our method is applicable to various problems with multitone driving schemes in cavity optomechanics, electromechanics, and related disciplines. CONTENTS

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Quantum Backaction Evading Measurement of Collective Mechanical Modes

Cited by 107 publications

References 44 publications

A correlated electromechanical system

A correlated electromechanical system

Force sensing in hybrid Bose-Einstein-condensate optomechanics based on parametric amplification

Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

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